Multiple-antenna wireless, also known as MIMO (multiple-input, multiple-output), remains an exciting area of communications research. MIMO promises the potential of orders-of-magnitude improvement in throughput compared with single-antenna links, without requiring extra power or physical bandwidth (see, e.g., Foschini, “Layered Space-Time Architecture for Wireless Communication in a Fading Environment when Using Multi-Element Antennas,” Bell Labs. Tech. J., vol. 1, no. 2, pp. 41-59, 1996, incorporated herein by reference, and, Telatar, “Capacity of Multi-Antenna Gaussian Channels,” European Transactions on Telecommunications, Vol. 10, No. 6, November 1999, incorporated herein in its entirety).
Bell Laboratories Layered Space-Time, or BLAST (see, Foschini, et al., supra) was the first practical scheme for realizing large throughputs with multiple antennas. BLAST assumes that the propagation matrix, the matrix-valued transfer function that couples the transmit array to the receive array, is constant with respect to frequency over the bandwidth of the transmitted signals (a condition known as “flat-fading”), and constant over relatively long intervals of time (the “coherence interval”) as well. The condition can usually be guaranteed by using a sufficiently narrow bandwidth. For a general discussion of fading, see Biglieri, et al., “Fading Channels: Information-Theoretic and Communications Aspects,” IEEE Trans. Info. Theory, vol. 44, no. 6, pp. 2619-2992, October 1998, incorporated herein by reference in its entirety.
The receiver estimates the propagation matrix from known training signals sent by the transmitter. The propagation matrix is then used to perform BLAST decoding. For many scenarios, the training interval occupies a negligible fraction of the coherence interval (see, Marzetta, “BLAST Training: Estimating Channel Characteristics for High-Capacity Space-Time Wireless,” Proc. 37th Annual Allerton Conference on Communications, Control, and Computing, pp. 958-966, Monticello, Ill. , Sep. 22-24, 1999, incorporated herein by reference). However, fast-changing mobile environments can exceed the limits of training-based schemes with large numbers of transmit antennas.
This motivated the development of unitary space-time modulation (USTM) (see, Hochwald, et al., “Unitary Space-Time Modulation for Multiple-Antenna Communications in Rayleigh Flat Fading,” IEEE Trans. Info. Theory, vol. 46, no. 2, incorporated herein in its entirety, and, U.S. Pat. No. 6,363,121, issued on Mar. 26, 2002, and entitled “Wireless Transmission Method for Antenna Arrays Using Unitary Space-Time Signals,” incorporated herein by reference) which dispenses entirely with training.
In lieu of training, message bits are encoded onto a L×M unitary matrix that is transmitted over L consecutive symbols, with M equal to the number of transmit antennas and L≧2M. A noncoherent receiver that requires no knowledge of the propagation matrix, and that only assumes that the propagation matrix is constant over the L symbols, performs the decoding.
Differential unitary space-time modulation (see, Hughes, “Differential Space-Time Modulation,” IEEE Trans. Info. Theory, vol. 46, no. 7, pp. 2567-2578, November 2000, Hochwald, et al., “Differential Unitary Space-Time Modulation,” IEEE Trans. Commun., vol. 48, no. 12, pp. 2041-2052, December 2000, and U.S. patent application Ser. No. 09/356,387 filed Jul. 16, 1999, entitled “Method for Wireless Differential Communication Using Multiple Transmitter Antennas,” all incorporated herein by reference, and, Marzetta, supra) is a special case where L=2M and where the matrix-valued signals have a particular structure such that the last L/2 symbols of a signal are identical to the first L/2 symbols of the next signal. Only the nonredundant part of the signal has to be transmitted, so in effect each L×M unitary matrix occupies only L/2 symbols, which tends to offset the 50% redundancy of the structured L×M signal. Differential Unitary Space-Time Modulation generates a sequence of M×M unitary transmitted signals, {S0, S1, . . . }, where S0=I (the M×M identity matrix), and Sk=Ak S{k−1}, k=1, 2, . . . , where {A1, A2, . . . } is a sequence of M×M unitary matrices that are obtained from the message bits.
As with USTM, a noncoherent receiver performs the decoding under the assumption that the propagation matrix is constant over L consecutive symbols. Decoding of the kth signal is based on the kth and the (k−1)th received signals, which (excluding noise) are equal to Ak S{k−1} H and S{k−1} H respectively, where H is the unknown M×N propagation matrix. The product S{k−1} H is assumed unknown, but the combination of the two measurements and the internal structure of the unitary matrix Ak permits decoding.
At present, techniques for designing constellations of differential USTM signals and efficient decoding algorithms are more developed than for the more general nondifferential USTM (see, Hochwald, et al., “Cayley Differential Unitary Space-Time Codes,” submitted to IEEE Trans. Info. Theory, February 2001, incorporated herein by reference in its entirety) though recent progress in nondifferential techniques has been reported (see, Hassibi, et al., “Unitary Space-Time Modulation via the Cayley Transform,” Proceeding 2002 IEEE International Symposium on Information Theory, Lausanne, Switzerland, Jun. 30-Jul. 5, 2002, incorporated herein by reference in its entirety).
Cayley modulation is based on the Cayley representation for the unitary matrix Ak=(I−i Qk) (I+i Qk)−1, where I is the M×M identity matrix, and Qk is an M×M conjugate symmetric matrix. In turn, Qk is a linear combination of M×M conjugate symmetric basis matrices, where the scalar weights depend on the message bits. Like BLAST, both USTM and differential USTM assume a condition of flat-fading.
Higher bandwidths, such as the 5 MHz used in Third Generation (3G) wireless, usually invalidate the flat-fading assumption, leaving receivers to deal with an unknown propagation matrix that is a function of frequency. Accordingly, what is needed in the art is still further improvement in MIMO modulation techniques. More specifically, what is needed is a MIMO modulation technique that dispenses with the need for a flat-fading assumption and therefore accommodate higher bandwidths in fading environments.